"What we want is, and I'm not going to give you a stage in the tournament... but, I'm going to give it away slightly, we haven't won a knockout game since 2006," the FA's chief executive Martin Glenn told the Daily Telegraph.
"So, clearly, getting out of the group and winning a knockout game would be a real sign of progress. And if you win one, you win more."
England are in Group G with much-fancied Belgium, Panama and Tunisia.
The 1966 World Cup winners failed to get out of the group in 2014, when they were defeated by Italy and Uruguay, and lost 4-1 to Germany in the round of 16 in 2010.
They last won a knockout tie in 2006, against Ecuador, when they reached the quarter-finals.
Should England qualify from their group they will face either Poland, Senegal, Colombia or Japan from Group H.
Another win might pit them against either Brazil or the holders Germany in the last eight.
England have impressed in warm-up wins over fellow World Cup teams Nigeria and Costa Rica.
